Since its inception in 1972 [1]}, Stein's method has been utilised in many research areas to provide a foundation for distributional comparison and approximation. The main objective of such a problem is to bound the (pseudo-) metric
\( d_{\mathcal {H}}(P,Q):= \sup _{h \in \mathcal {H}}\bigg | \int h dP - \int h dQ \bigg | \) 
